Question

write an equation that gives the amount of snow that has fallen after X hours at this rate use the form y= xk).​

Answer 1

Given:

After 2 hours, the amount of snow fall is 6 inches.

To find:

We need to write an equation that gives the amount of snow that has fallen after $x$ hours.

Solution:

Let $x$ represents the time and $y$ represents the amount of snow fall.

We know that, as time increases, the amount of snow fall also increases.

So,

$\Rightarrow x \ \alpha \ y$

$\Rightarrow y \ \alpha \ x$

$\Rightarrow y=kx$.......Equation (i)

Where $k$ is the proportionality constant.

Here, to complete the above equation, it is required to find the value of  $k$.

Given that, after 2 hours, the amount of snow fall is 6 inches.

So,

$\Rightarrow y=kx$

$\Rightarrow 6=k(2)$

$\Rightarrow 3=k$

$\Rightarrow k=3$

Now, substitute the value of $k$ in equation (i).

$\Rightarrow y=3x$

Therefore, the required equation is $y=3x$.